Re:Physics is unreasonably good at creating new math
by Joker_vD on Wednesday September 04, 2024 @04:54PM
(#41450692)
> But you'd only attempt that if you thought there was something questionable in the first place.
No, that's not the only reason. Come on, people actually wrote why they tried to prove it in their commentaries on Euclid's Elements.
For example, some people found that this postulate, compared with the first four, is not really that self-evident and also has a sudden jump in the complexity of its formulation. That's why some courses on geometry replaced it with something different (but equivalent), like "the sum of angles of any triangle is 180 degrees", or "for a line and a point not on it, there is exactly one line parallel to it that passes through that point", or "there are triangles with arbitrary large areas", etc.
No, that's not the only reason. Come on, people actually wrote why they tried to prove it in their commentaries on Euclid's Elements.
For example, some people found that this postulate, compared with the first four, is not really that self-evident and also has a sudden jump in the complexity of its formulation. That's why some courses on geometry replaced it with something different (but equivalent), like "the sum of angles of any triangle is 180 degrees", or "for a line and a point not on it, there is exactly one line parallel to it that passes through that point", or "there are triangles with arbitrary large areas", etc.